On interval estimates of perturbations of generalized eigenvalues for diagonalizable pairs

On generalized eigenvalue perturbation bounds for diagonalizable matrix pairs upper bounds are discussed all the time. In this paper we mainly consider not only upper bounds but also lower bounds of perturbation of generalized eigenvalues for diagonalizable matrix pairs. Sharper upper bounds and sharp lower bounds on perturbation of generalized eigenvalues for diagonalizable matrix pairs are obtained in terms of the distances of two points in Grassmann manifold. The main results improve the existing results of Chen (2007) [1] and numerical examples illustrate the efficiency of the theoretical results.